Abstract

Diffuse Optical Imaging (DOI), the study of the propagation of Near Infra-Red (NIR) light in
biological media, is an emerging method in medical imaging. Its state-of-the-art is non-invasive,
versatile and reasonably inexpensive.
In Diffuse Optical Tomography (DOT), the adaptation of numerical methods such as the
Finite Element Method (FEM) and, more recently the Boundary Element Method (BEM), has
allowed the treatment of complex problems, even for in vivo functional three-dimensional imaging.
This work is the first attempt to combine these two methods in DOT.
The BEM-FEM is designed to tackle layered turbid media problems. It focuses on the region
of interest by restraining the reconstruction to it. All other regions are treated as piecewise-constant
in a surface-integral approach. We validated the model in concentric spheres and found
that it compared well with an analytical result. We then performed functional imaging of the
neonate’s motor cortex in vivo, in a reconstruction restricted to the brain, both with FEM and
BEM-FEM.
Another use of the BEM in DOI is also outlined. NIR Spectroscopy (NIRS) devices are
particularly used in brain monitoring and Diffuse Optical Cortical Mapping (DOCM). Unfortunately,
they are very often accompanied by rudimentary analysis of the data and the 3D appreciation
of the problem is missed. The BEM DOCM developed in the current work represents an
improvement, especially since a topographical representation of a motor activation in the cortex
is clearly reconstructed in vivo.
In the interest of computational speed an acceleration technique for the BEM has been
developed. The Fast Multipole Method (FMM), which is based on the decomposition of Green’s
function on a basis of Bessel and Hankel functions, eases the evaluation of the BEM matrix,
along with a faster calculation of the solutions.